Recent progress in the theoretical treatment of electronically nonadiabatic processes is discussed. First we discuss the generalized Born–Oppenheimer approximation, which identifies a subset of strongly coupled states, and the relative advantages and disadvantages of adiabatic and diabatic representations of the coupled surfaces and their interactions are considered. Ab initio diabatic representations that do not require tracking geometric phases or calculating singular nonadiabatic nuclear momentum coupling will be presented as one promising approach for characterizing the coupled electronic states of polyatomic photochemical systems. Such representations can be accomplished by methods based on functionals of the adiabatic electronic density matrix and the identification of reference orbitals for use in an overlap criterion. Next, four approaches to calculating or modeling electronically nonadiabatic dynamics are discussed: (1) accurate quantum mechanical scattering calculations, (2) approximate wave packet methods, (3) surface hopping, and (4) self-consistent-potential semiclassical approaches. The last two of these are particularly useful for polyatomic photochemistry, and recent refinements of these approaches will be discussed. For example, considerable progress has been achieved in making the surface hopping method more applicable to the study of systems with weakly coupled electronic states. This includes introducing uncertainty principle considerations to alleviate the problem of classically forbidden surface hops and the development of an efficient sampling algorithm for low-probability events. A topic whose central importance in a number of quantum mechanical fields is becoming more widely appreciated is the introduction of decoherence into the quantal degrees of freedom to account for the effect of the classical treatment on the other degrees of freedom, and we discuss how the introduction of such decoherence into a self-consistent-potential approximation leads to a reasonably accurate but very practical trajectory method for electronically nonadiabatic processes. Finally, the performances of several dynamical methods for Landau–Zener-type and Rosen–Zener–Demkov-type reactive scattering problems are compared.

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Introductory lecture: Nonadiabatic effects in chemical dynamics

Fast-switching displays with memory properties are provided, which can display digits, symbols, and images, and which contain as chemically and thermally stable ferroelectric liquid crystalline substances, according to the invention, liquid crystalline derivatives which contain a chiral alkyl halide residue corresponding to the general formula ##STR1## are used in mixtures of one another as well as in conjunction with other liquid crystalline or non-crystalline liquid substances.

Ferroelectric liquid crystals

We characterize three nonstandard electrohydrodynamic instabilities in nematic liquid crystals composed of bent-core molecules In addition to their shape, another important attribute of this material is that the anisotropy in the electrical conductivity changes sign as the frequency of the applied electric field changes These instabilities do not appear to fit within the standard model for electroconvection The first instability creates a pattern with stripes parallel to the initial director orientation, with a wavelength about equal to the separation of the cell plates The next is the previously reported prewavy instability The third instability is optically and dynamically identical to the prewavy instability, but is distinguished by different threshold behavior

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Nonstandard electroconvection in a bent-core nematic liquid crystal.

Electric field-induced patterns in liquid crystals have been observed and studied for about 50 years During this time, a great variety of structures, detected under different conditions, have been described; theoretical descriptions were also developed parallel with the experiments and a huge number of papers have been published The non-vanishing interest in the topic is due to several factors First, most experimentalists working with new (or even well-known) liquid crystals apply sooner or later an electric field for different purposes and, as a response, often (maybe undesirably or unexpectedly) have to face with emergence of patterns Second, understanding the complexity of the formation mechanism of regular patterns in a viscous, anisotropic fluid is an extremely challenging theoretical task Third, specialists in display fabrication or in other applications are also interested in the results; either to make use of them or in order to avoid field-induced patterns In this review, we attempt

Electrically induced patterns in nematics and how to avoid them

The performance of an analytical expression for algorithmic decoherence time is investigated for non–Born–Oppenheimer molecular dynamics. There are two terms in the function that represents the dependence of the decoherence time on the system parameters; one represents decoherence due to the quantum time-energy uncertainty principle and the other represents a back reaction from the decoherent force on the classical trajectory. We particularly examine the question of whether the first term should dominate. Five one-dimensional two-state model systems that represent limits of multidimensional nonadiabatic dynamics are designed for testing mixed quantum-classical methods and for comparing semiclassical calculations with exact quantum calculations. Simulations are carried out with the semiclassical Ehrenfest method (SE), Tully’s fewest switch version (TFS) of the trajectory surface hopping method, and the decay-of-mixing method with natural switching, coherent switching (CSDM), and coherent switching with rei...

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Algorithmic decoherence time for decay-of-mixing non-Born-Oppenheimer dynamics

Total solution of flexoelectric instability problem is given for finite thickness sample and real elastic moduli. There is a linear coupling between electric polarization and orientational deformation in nematic liquid crystal [l]. The appropriate term in the free energy of liquid crystal under the influence of electric field E can be written in accordance with symmetry properties as where n(r) is director, e, and e2 are flexoelectric moduli. This coupling results in appearance peculiar flexoelectric effect which is a periodic distortion of initial planar orientation. Meier [l] had shown that the infinite liquid crystal must be disturbed and the perturbation must be periodic along the director orientation in the absence of electric field. This deformation is not the threshold one and its period is inversely proportional to electric field strength. It was shown in the paper [2] that another type of flexoelectric instability is possible in nematic liquid crystal layers of finite thickness with a homogeneous orientation on the walls. New instability arising at certain threshold voltage is characterized by small director deviations from X axis in two planes : on angle 8 in XZ plane and on angle p in XY plane (see Fig. 1). The instability results in arising of the periodic along Y axis domain structure which is parallel to X axis. In the case of small deformations lp l , 181 + l ,n, = l , n y = p , n , = 0, E, = E, = 0, E, = E and equal elastic moduli K,, = K,, = K the solution corresponding to the boundary conditions 0 = p = 0 at z = + d/2 takes the form : 8 = 8, cos (qy) cos (nzld) , cp = cpo sin (qy) cos (nzld) . (2) The instability appears at the threshold voltage U, and the threshold wave vector q, : where p = (E, K/4 ne# ') , e# = e1 e 2 , E, is dielectric anisotropy, d is the layer thickness. Similar flexoelectric instability can exist under the influence of constant as well as alternating electric field. Frequency dependence of the threshold is analysed in reference [2]. Such type of instability seems to be observed for the first time by Vistin 131. Perhaps this instabiIity can be observed in alternating field at temperatures when the Williams domains do not exist because of negative sign of conductivity anisotropy [4]. Arising of this flexoelectric instability in constant field and the dependence of threshold voltage and wave vector upon dielectric anisotropy were investigated in reference [5] in details using n-buty1-n\"methoxyazoxybenzol doped by 2-3-dicyano-4-amyloxyphenyl ester of amyloxybenzoic acid or nucyanphenyl ester of n-heptylbenzoic acid for changing of dielectric anisotropy. The experimental data are in good agreement with the theory and allow one to define K and e# for BMAOB taking E, < 0 (K = 6.5 X 10-' dyne, FIG. I. Distribution of molecular orientation. e# = 1.7 X 10-4 CGS units) . Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979364 C3-332 Y. P. BOBYLEV, V. G. CHIGRINOV AND S. A. PIKIN The equations (3) were received for equal moduli Kjj so only average values of Kjj and e\" were determined in reference [5]. The purpose of the present paper is the investigation of threshold characteristics of flexoeffect using real values of elastic moduli. In the case of small deformations 1cp 1 , 1 f 3 1 < 1 the free energy of nematic can be written as Let us take the solution satisfying to boundary conditions 8 = cp = 0 at z = + d/2 as cp = 9 0 sin (qy) exp(ipz) 9 8 = 8, cos (qy) exp(ipz) . (6) Inserting (6) into (5) and taking into account the condition of nontriviality of 8, and p, values one can write the following equation for characteristic numbers p : where s = plq, p = ((E, K1 1/4 ne# ,), a = K2,/Kl1, 5 = e# E/Kl l g. Equation (7) has 4 roots : f S,, f S,. So one get the complete solution of equation (5) in the form :

https://hal.archives-ouvertes.fr/docs/00/21/87/60/PDF/ajp-jphyscol197940C364.pdf

Threshold flexoelectric effect in nematic liquid crystal

Experimental verification of the theory of electrohydrodynamic instability in nematic liquid crystals

A condition for obtaining bistable states in a liquid-crystalline ferroelectric (S*C) has been found by computer simulation and analytical estimates; it depends on the value of the applied electric field, the magnitude of the polar contribution to anchoring energy and the material parameters of S*C

S. A. Pikin

Papers

Threshold flexoelectric effect in nematic liquid crystal

Experimental verification of the theory of electrohydrodynamic instability in nematic liquid crystals

Bistable and monostable polarized states of a liquid-crystalline ferroelectric in an electric field

Threshold piezoelectric instability in a liquid crystal

Electrohydrodynamic Instability in Nematic Liquid Crystals